Metric theory for a new family of continued fraction expansions – Niels Langveld (TU Delft)

Venue

Sala Riunioni (Puteano, Centro De Giorgi).

Abstract

The family of flipped expansions and the family of 2-expansions is combined to make a new family of continued fraction expansions we will call flipped 2-expansions. It is shown that there is only one flipped continued fraction expansion map that will produce only even digits and only one map which will produce only odd digits. Similarly we find only one map for which the 2-expansion of every number will have odd digits. When combining, we obtain for every real number infinitely many expansions with only odd or only even digits. Some examples of flipped 2-expansions are given and a method for finding the invariant measure using the natural extension is explained. This work is the result of my graduation project supervised by Cor Kraaikamp.

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